The invention relates to a circuit arrangement for defining the positions of extrema of a correlation function of two signals which are present in a digital form.
A circuit arrangement of this type can be used, for example, for measuring the shift of two speech signals as a function of time. In such a case the two signals, whose correlation is to be determined, are only dependent on one (time) variable. Also the correlation function itself is a function of one variable only, namely of the mutual time shift of the two signals.
An example of using signals which are dependent on two variables is found in picture encoding. In order to reduce the bit rate in a picture encoder (cf., for example, DE 37 26 520 A1), it is checked which section of a picture already transmitted (first signal) is most correlative with a section (second signal) of the actual picture. In this case the signals are functions of two coordinates and the correlation function is a function of the two shifts, each in a direction of the two coordinates axes.
For the sake of formal simplicity the following description will only consider the case in which the signals are dependent on one variable, because an extension to a plurality of variables will be evident to those skilled in the art.
The correlation function A of two signals f and g which are present in a digital form is herein understood to mean any function of the type ##EQU1## in which k is a normalization constant, i and .mu. are integers, while f(i) and g(i-.mu.) represent the sampling values of the functions f and g at the instants which are symbolized by the integral numbers i and i-.mu.. A(.mu.) is then a sampling value of the correlation function at the instant .mu.. .mu. is simultaneously the shift of the function g with respect to its original position. The number of the shifts .mu. considered is limited: .mu. may assume any integral number between -p and p, where p is also an integral number and may have different values from case to case. p defines the so-called search range in which, for example, an extremum of A(.mu.) is searched. F denotes a combination of the two functions f and g which is not further identified. The reference b denotes the number of the terms of the sum in (1).
When evaluating formula (1), the arguments of the function can also be interpreted as symbols of the memory addresses under which the relevant sampling values are stored. The relevant interpretation will be evident from the context and will not be explicitly mentioned.
Use of the product of the functions f and g for the combination F results in the correlation function of the two functions f and g. The two functions f and g have their greatest correlation for that value of the shift .mu. for which the correlation function assumes its maximum value.
If the value itself or the square value of the difference is used for F, the functions f and g have their greatest correlation for that value of .mu. for which A(.mu.) assumes a minimum value. The choice of the combinations F in individual cases is dependent on the attendent circumstances of the case and will not be further discussed.
Not only are the largest or the smallest value of the correlation function A(.mu.) and its position .mu.e frequently important, but also the next smaller values in the case of a maximum and the next larger values in the case of a minimum, as well as the positions of these values. The extreme value combined with the next values--as mentioned hereinbefore--will be referred to as extrema.
In the direct evaluation of formula (1), 2pb+b times the combination F for different values of the functions f and g is to be defined when defining the extrema and their positions. This may involve elaborate computations in many applications.